Vanishing of Poincar\'e series for congruence subgroups
Abstract
We consider the problem of the vanishing of Poincar\'e series for congruence subgroups. Denoting by Pk,m,N the Poincar\'e series of weight k and index m for the group 0(N), we show that for certain choices of parameters k,m,N, the Poincar\'e series does not vanish. Our methods improve on previous results of Rankin (1980) and Mozzochi (1989).
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